Flexible Linear and Angular Displacement Sensor Based on a Gradient Guided-Mode Resonance Filter

This paper reports a method for micrometer-scale linear and angular displacement measurement based on a gradient grating period guided-mode resonance (GGP-GMR) filter. When the filter is mounted on a moving or rotating object, the displacement on the object can be observed through the changes in the resonant wavelength, which are detected by the GGP-GMR filter. In this paper, the GGP-GMR filter comprised grating periods from 250 to 550 nm with 2-nm increments. Each period comprised 100 repeated cycles, resulting in a total length of 6 mm. For linear displacement, we achieved an average sensitivity of 67 nm/mm for a detection range of 6 mm and a theoretical limit of detection of 3 μ. To demonstrate the measurement of angular displacement, the GGP-GMR filter was attached to a cylinder with a diameter of 8 cm. The experimental results revealed an average sensitivity of 51.7 nm/° for a range of 7° and an experimental limit of detection of 0.002°.